The present invention is directed to a method for recovering a signal to control the phase of a local carrier signal in such a manner that the local carrier signal and the carrier signal of an amplitude and/or phase shift keyed received signal are in phase synchronism. More particularly, the present invention is directed to a control signal recovery method of the type which includes the steps of dividing the local carrier signal into two at least approximately orthogonally oriented local carrier components which represent the axes of a signal state plane having four quadrants; mixing the received signal with the two local carrier signal components to produce two mixed signals which represent projections of received signal states on the coordinate axes of the signal state plane; using the two mixed signal components to address a memory having a plurality of memory locations in order to read out the content of a memory location for each received signal state, the memory locations corresponding to quantized regions into which the signal state plane is divided by way of quantization thresholds extending parallel to the two coordinate axes, predetermined ones of the quantization thresholds intersecting at predetermined points which correspond to permitted signal states that might have been transmitted, each memory location storing a numerical value which is representative of a phase deviation between a corresponding quantized region and the closest predetermined point; and averaging numerical values read out of the memory for a plurality of received signal states to produce the control signal.
Such a method is disclosed in an article by M. Hoffmann, entitled "Carrier Recovery for a m-QAM Signals" in the proceedings of the European Conference of Radio Relay Systems (ECRR), pages 247-253, published by vde-verlag, Munich, November, 1986. This method is used to obtain a control signal for a voltage controlled oscillator used to recover the carrier in a demodulator circuit for amplitude and/or phase shift keyed QASK signals.